Effect of anelastic patchy saturated sand layers on the reflection and transmission responses of a periodically layered medium

Based on analytic relations, we compute the reflection and transmission responses of a periodically layered medium with a stack of elastic shales and partially saturated sands. The sand layers are considered anelastic (using patchy saturation theory) or elastic (with effective velocity). Using the patchy saturation theory, we introduce a velocity dispersion due to mesoscale attenuation in the sand layer. This intrinsic anelasticity is creating frequency dependence, which is added to the one coming from the layering (macroscale). We choose several configurations of the periodically layered medium to enhance more or less the effect of anelasticity. The worst case to see the effect of intrinsic anelasticity is obtained with low dispersion in the sand layer, strong contrast between shales and sands, and a low value of the net‐to‐gross ratio (sand proportion divided by the sand + shale proportion), whereas the best case is constituted by high dispersion, weak contrast, and high net‐to‐gross ratio. We then compare the results to show which dispersion effect is dominating in reflection and transmission responses. In frequency domain, the influence of the intrinsic anelasticity is not negligible compared with the layering effect. Even if the main resonance patterns are the same, the resonance peaks for anelastic cases are shifted towards high frequencies and have a slightly lower amplitude than for elastic cases. These observations are more emphasized when we combine all effects and when the net‐to‐gross ratio increases, whereas the differences between anelastic and elastic results are less affected by the level of intrinsic dispersion and by the contrast between the layers. In the time domain, the amplitude of the responses is significantly lower when we consider intrinsic anelastic layers. Even if the phase response has the same features for elastic and anelastic cases, the anelastic model responses are clearly more attenuated than the elastic ones. We conclude that the frequency dependence due to the layering is not always dominating the responses. The frequency dependence coming from intrinsic visco‐elastic phenomena affects the amplitude of the responses in the frequency and time domains. Considering intrinsic attenuation and velocity dispersion of some layers should be analyzed while looking at seismic and log data in thin layered reservoirs.     

Effect of surface wave propagation in a four-layered oceanic crust model

Dispersion of Rayleigh type surface wave propagation has been discussed in four-layered oceanic crust. It includes a sandy layer over a crystalline elastic half-space and over it there are two more layers—on the top inhomogeneous liquid layer and under it a liquid-saturated porous layer. Frequency equation is obtained in the form of determinant. The effects of the width of different layers as well as the inhomogeneity of liquid layer, sandiness of sandy layer on surface waves are depicted and shown graphically by considering all possible case of the particular model. Some special cases have been deduced, few special cases give the dispersion equation of Scholte wave and Stoneley wave, some of which have already been discussed elsewhere.     

NON-NORMAL INCIDENCE STATE-SPACE MODEL AND LINE SOURCE REFLECTION SYNTHETIC SEISMOGRAM*

This paper is directed at modeling layered media. We extend the plane-wave normal-incidence state-space model developed by Mendel, Nahi and Chan in 1979, to the non-normal incidence case. To do this we introduce a shifting principle, a zero-offset wavefront, and zero-offset travel times for different layers. We also develop an algorithm for obtaining a synthetic line source reflection seismogram. In this algorithm non-normal incidence plane-wave seismograms are summed over a range of incident angles. The algorithm is based on a modified version of Sommerfield's (1896) theorem. Simulations of acoustic and elastic media are included which illustrate the applicability of our plane-wave and line source seismograms for both elastic and acoustic cases.     

Distinguishing oil and water layers by interpreting acoustic logging data with changing well diameters

During surveys, water layers may interfere with the detection of oil layers. In order to distinguish between oil and water layers, research on the properties of well diameters and oil and water layers and their relation to acoustic logging rules is essential. Using Hudson's crack theory, we simulated oil and water layers with different well diameters or crack parameters (angle and number density). We found that when the well radius increases from 0.03 m to 0.05 m, the variation ratio of compressional wave amplitude for the oil layer is less than that for the water layer. The difference of Stoneley wave amplitude between the crack parameters (angle and number density) is greater in the case of the water layer than in the case of the oil layer. The response sensitivity of wave energy is greater for the water layer than that for the oil layer. When the well radius increases from 0.05 m to 0.14 m, the maximum excitation intensity for oil layer is greater than that for the water layer. We conclude that the propagation of an elastic wave is affected by medium composition and well diameter, and the influence has certain regularity. These results can guide further reservoir logging field exploration work.     

Modelling gravity variations consistent with ground deformation in the Campi Flegrei caldera (Italy)

In recent years (1970–72 and 1982–84) two inflation episodes took place in the Campi Flegrei caldera (Italy), characterized by significant ground uplift and gravity variations. An elastic half-space model with vertical density stratification is employed to compute the displacement field and the gravity variations produced by the deformation of buried layers, following the inflation of a spherically symmetric deformation source. Contributions to gravity variations are produced by dilation/contraction of the medium, by the displacements of density interfaces (the free surface and subsurface layers) and of source boundaries and, possibly, by new mass input from remote distances into the source volume. Three cases were examined in detail: In case I, the magma chamber is identified as the deformation source and volume and pressure increase in the magma chamber is due to input of new magma from remote distances; in case II deformation is due to magma differentiation within the magma chamber (deformation source with constant mass); in case III the geothermal system is identified as the deformation source and a pressure increase, possibly driven by the exsolution of high temperature and high pressure volatiles in the magma chamber, is assumed to play a dominant role. From the comparison between measured and computed gravity residuals (free-air-corrected gravity variations) we can assess that, in case I, an inflation source with constant density would predict gravity residuals compatible with observations, whereas an expansion at constant mass (case II) would predict gravity residuals much lower than observed. The resolving power of gravity data however prevents accurate assessment of the density of the emplaced material. In case III, the pervasive density increase of the geothermal fluids induced by pressure increase is assumed to be the main source of gravity variations. The average porosity value required for this model to match both the ground deformation and the gravity residuals is found to be ˜10%, a value which is compatible with measured porosity values at Campi Flegrei in deep wells. The subsidence phases following both inflation episodes and the gravity residuals during subsidence lead us to consider case III as more plausible, even if a suitable combination of cases I and III cannot be discarded.     

Moveout approximation for horizontal transversely isotropic and vertical transversely isotropic layered medium. Part I: 1D ray propagation‡

Anisotropy in subsurface geological models is primarily caused by two factors: sedimentation in shale/sand layers and fractures. The sedimentation factor is mainly modelled by vertical transverse isotropy (VTI), whereas the fractures are modelled by a horizontal transversely isotropic medium (HTI). In this paper we study hyperbolic and non‐hyperbolic normal reflection moveout for a package of HTI/VTI layers, considering arbitrary azimuthal orientation of the symmetry axis at each HTI layer. We consider a local 1D medium, whose properties change vertically, with flat interfaces between the layers. In this case, the horizontal slowness is preserved; thus, the azimuth of the phase velocity is the same for all layers of the package. In general, however, the azimuth of the ray velocity differs from the azimuth of the phase velocity. The ray azimuth depends on the layer properties and may be different for each layer. In this case, the use of the Dix equation requires projection of the moveout velocity of each layer on the phase plane. We derive an accurate equation for hyperbolic and high‐order terms of the normal moveout, relating the traveltime to the surface offset, or alternatively, to the subsurface reflection angle. We relate the azimuth of the surface offset to its magnitude (or to the reflection angle), considering short and long offsets. We compare the derived approximations with analytical ray tracing.     

台址下表层介质电阻率变化对视电阻率观测值影响特征的初步研究

气候的交替变化将导致大地表层含水量发生变化，从而使该层介质的电阻率发生变化，进而使得观测结果(即视电阻率)发生变化，显然这对地震前兆观测而言是一种干扰。目前我国绝大多数前兆地电阻率台采用单极距观测方式，因此观测到的视电阻率变化应是表层变化(主要是干扰)和观测范围内深部变化(地下介质应力与应变状态发生变化)的综合反映。作先依据台址下的水平层状模型进行了模拟计算研究，发现大地表层含水量的变化对单极距四极装置视电阻率观测值的影响有两个特征：(1)无论台址下电阻率结构是下伏低阻还是下伏高阻，表层介质电阻率升高对观测值的影响都很小；(2)表层电阻率降低对观测值的影响很明显，且对下伏高阻结构的影响大于对下伏低阻结构的影响。然后用视电阻率实际观测资料说明了将其特征用于预报的可能性。     

Effective bulk modulus of the pore fluid at patchy saturation

We explore a package of parallel porous layers, each filled with a different fluid. Assume that this package is sampled by an elastic wave with the wavelength much larger than the thickness of an individual layer. Also assume that the layers are hydraulically isolated from each other, meaning that the diffusion length is smaller than that of the individual layer. This assumption is relevant to a patchy saturation scenario. Suppose that we wish to conduct the fluid substitution operation on this package treated as a single porous elastic body. What is the effective bulk modulus of the pore fluid to be used in this operation that will result in the same elastic modulus as computed by Backus averaging the individual moduli of the layers? We address this question analytically by assuming that the porosity, dry frame, and the mineral matrix properties of the individual layers are the same for all layers. The only difference between the layers is the pore fluid. We find that the resulting effective bulk modulus of the fluid thus derived falls between the arithmetic and harmonic averages of the fluid bulk moduli in the layers. It can be approximated by a linear combination of these two bounds where the weights are 0.50 and 0.50 or 0.75 for the arithmetic average and 0.25 for the harmonic average, depending on the elastic moduli of the dry frame, the mineral, and the pore fluids. This solution also provides a relation between the effective bulk modulus of the pore fluid in the system under examination and water saturation to be used in the fluid substitution operation at a coarse spatial scale.     

鄂尔多斯块体西南定边-大罗山大地电磁剖面解释

鄂尔多斯块体定边—大罗山段大地电磁结果表明，鄂尔多斯块体内部电性结构简单，成层性好，上地幔第一高导层顶面埋深基本在１０９ｋｍ左右，相当平坦，块体内部不存在壳内高导层。而靠近大罗山处，上地幔第一高导层向上隆起，隆起最高处距地表９２ｋｍ，此处测点壳内有电性分层，但由于断裂带的切割使测点之间的壳内分层不易连接，形成不连续层。分析认为该处为深大断裂带，是鄂尔多斯块体的西部边界     

Coseismic and postseismic subsurface displacements and strains for a vertical strike-slip fault in a three-layer elastic medium

A three-layer elastic-gravitational fault displacement model using dislocation theory has been developed and used to examine the effect of layering of earth elastic moduli on surface and subsurface displacement fields for a vertical strike-slip fault. The model has been used to examine the effect of depth variation of elastic properties at coseismic and postseismic time scales. For pure strike-slip motion the effect of gravity on coseismic and postseismic horizontal deformation is negligible. For coseismic deformation the model predicts that (for constant Poisson's ratio) an increase in elastic moduli with depth attenuates the displacements within the upper layers with respect to displacement distribution for a uniform half-space, while an inclusion of a soft layer between the top layer and lower half-space amplifies upper layer displacements. The effect of variation in Poisson's ratio on surface and subsurface displacements has also been examined.The effect of postseismic stress relaxation on surface and subsurface displacements for a three-layer model has been calculated and compared with that of a uniformly relaxed half-space model. Layer 1 is assumed to correspond to the upper crust, layer 2 the lower crust and layer 3 the upper mantle. The effect of postseismic stress relaxation within a uniform half-space and within just the lower crust and upper mantle has been examined. Stress relaxation within the whole half-space decreases the amplitude and shortens the wavelength of displacements, while stress relaxation within the lower two layers increases the amplitude and broadens the wavelength of displacements. The difference between uniform and layered postseismic relaxation is particularly pronounced at the base of the crust.Coseismic and postseismic normal and volumetric strains for a vertical strike-slip fault have also been examined. For a uniformly relaxed half-space model, an increase in normal strains is shown with respect to the coseismic elastic solution, whereas the postseismic volumetric strain is effectively zero. For a three-layer model with stress relaxation in the lower layers only, the normal and volumetric strains within the top elastic layer resemble coseismic strains, while in the lower layers which suffer a rigidity decrease, the postseismic volumetric strain is effectively zero.     

华南东部吉安—福州剖面岩石圈电性结构研究

为了研究华南东部地区岩浆活动的深部构造背景,对吉安一福州宽频大地电磁测深剖面数据进行了系统的分析和处理,并利用非线性共轭梯度法进行二维反演,得到了武夷隆起带及周缘地区的岩石圈电性结构;结合区域重磁资料,详细分析了研究区内地壳、上地幔电性结构特征及地质含义.结果表明:华南东部地区岩石圈电性结构存在明显的分区性,并且壳内普遍发育不同成因的高导层,揭示出华南东部地区不同构造单元内的岩浆活动具有不同的成岩构造背景.其中,东南沿海褶皱带深部热侵蚀活跃,岩石圈物质和结构被强烈改造,电阻率普遍较低,软流圈上涌并伴随玄武岩浆底侵,导致岩石圈、地壳剧烈减薄;而武夷隆起带岩石圈电阻率相对较高,印支-燕山早期陆内挤压变形的构造形迹明显,晚中生代岩石圈拉张伸展作用对该地区岩石圈的物质结构有一定的改造.     

On disturbances in a piezoelectric layer permeated by a magnetic field

Summary The methods of transform calculus are made use of in finding the disturbances in a piezoelectric layer with an impulsive force at its free faces in presence of a magnetic field. The problem is solved for time dependent elastic compliance of the material of the layer.     

Rayleigh waves in granular medium

Summary The wave velocity equation in the form of a ninth order determinantal expression is derived appropriate to Rayleigh type waves in a granular half-space supporting a different granular layer. The calssical frequency equation when both media are elastic has been deduced as a particular case by limiting process.     

深层地震勘探的地震波传传播理论研究前景

深层地震勘探为地震波传播理论研究提出了新的挑战和机遇。深层地震勘探的主要难点是上覆层的影响甚大，使后续的处理有隔靴挠痒之感，必须应用波场延拓消除上覆层影响。深层波速的高速性和横向不均匀性决定了大角散射和弹性波处理方法的重要性。本文具体评述了深层地震勘探的主要方法对策，深入探讨了波场延拓的李群方法和弹性反演的某些问题，目的在于为深化深层地震提供新的研究手段和方法。     

Dispersion function of Rayleigh waves in porous layered half-space system

Rayleigh wave exploration is based on an elastic layered half-space model. If practical formations contain porous layers, these layers need to be simplified as an elastic medium. We studied the effects of this simplification on the results of Rayleigh wave exploration. Using a half-space model with coexisting porous and elastic layers, we derived the dispersion functions of Rayleigh waves in a porous layered half-space system with porous layers at different depths, and the problem of transferring variables to matrices of different orders is solved. To solve the significant digit overflow in the multiplication of transfer matrices, we propose a simple, effective method. Results suggest that dispersion curves differ in a lowfrequency region when a porous layer is at the surface; otherwise, the difference is small.     

Surface wave propagation in a transversely isotropic elastic layer overlying a liquid saturated porous solid half-space and lying under the uniform layer of liquid

Dispersion of Rayleigh-type surface wave is studied in a homogeneous transversely isotropic elastic layer overlying a nondissipative liquid-saturated porous solid half-space and lying under a uniform layer of homogeneous liquid. The frequency equation in the form of ninth-order determinant is obtained.Special cases have been deduced by reducing the depth of the layers to zero and by changing the transverse isotropic layer to an isotropic layer. Dispersion curves for the phase velocity have been plotted for a particular model.     

REFRACTION LE LONG DES BANCS MINCES RAPIDES ET EFFET D'ECRAN POUR LES MARQUEURS PROFONDS *

Refraction along thin high velocity layers and along basement is investigated in two cases. a) high velocity layer just on the basement. b) high velocity layer higher above. Period and attenuation of refracted waves are givers as a function of the layer thickness H. Refracted arrivals along thin high velocity layers are visible at significant distances if the layer thickness is not smaller than A/6, where A is the longitudinal wavelength in high velocity medium. The pseudoperiod is proportional to the layer thickness H. The attenuation at large distance follows an x^-ne^-k1x law, where n is close to I and k₁ is inversely proportional to H. Refracted arrivals along the basement are observable even in the case of thin high velocity layers situated in the overburden; their intensity is smaller and their pseudo-period larger than when no layer exists in the overburden. The intensity of the basement arrival decreases and the pseudoperiod increases with increasing layer thickness. The pseudoperiod and the attenuation of refracted arrivals along high velocity layers and along the basement are also highly dependent on acoustic contrasts. Both arrivals from a high velocity layer and from the basement can be recorded simultaneously, provided the frequency spectrum of the seismic chain is sufficiently broad. In all cases layer arrivals show a character very different from basement arrivals.     

Petrophysical properties of rocks in seismogenic crustal blocks of the southeastern Greater Caucasus and their geological and geophysical interpretation

The elastic and density properties of rocks of the Shamakha-Ismailly seismogenic blocks are studied by the ultrasonic pulse method in quasi-hydrostatic high pressure apparatuses. An attempt is made to more accurately determine the upper crustal lithology of these blocks. The observed values of the elastic and density characteristics of the rocks at high pressures suggest that the upper layers in the Ismailly and Shamakha blocks can consist of sedimentary carbonate rocks such as marls, sandstones, mudstones, and limestones. The middle layers apparently consist of volcaniclastic rocks: lithoclastic tuffs, andesites, etc. The lower layer (basement) in both blocks is likely composed of basic rocks such as basalts, trachybasalts, etc. According to the values of elastic wave velocities and densities, gabbroid rocks may compose the fourth layer of the Buinuz intrusion, identified from seismic data.     

Prediction of free field vibrations due to pile driving using a dynamic soil–structure interaction formulation

This paper presents a numerical model for the prediction of free field vibrations due to vibratory and impact pile driving. As the focus is on the response in the far field where deformations are relatively small, a linear elastic constitutive behaviour is assumed for the soil. The free field vibrations are calculated by means of a coupled FE–BE model based on a subdomain formulation. First, the case of vibratory pile driving is considered, where the contributions of different types of waves are investigated for several penetration depths. In the near field, the soil response is dominated by a vertically polarized shear wave, whereas in the far field, body waves are importantly attenuated and Rayleigh waves dominate the ground vibration. Second, the case of impact pile driving is considered. A linear wave equation model is used to estimate the impact force during the driving process. Apart from the response of a homogeneous halfspace, it is also investigated how the soil stratification influences the ground vibration for the case of a soft layer on a stiffer halfspace. When the penetration depth is smaller than the layer thickness, the layered medium has no significant influence on ground vibrations. However, when the penetration depth is larger than the layer thickness, the influence of the layered medium becomes more significant. The computed ground vibrations are finally compared with field measurements reported in the literature.     

Numerical analysis of seismic wave amplification in Nice (France) and comparisons with experiments

The analysis of site effects is very important since the amplification of seismic motion in some specific areas can be very strong. In this paper, the site considered is located in the centre of Nice on the French Riviera. Site effects are investigated considering a numerical approach (Boundary Element Method) and are compared with experimental results. The experimental results are obtained thanks to real earthquakes (weak motion) and microtremor measurements. The investigation of seismic site effects through numerical approaches is interesting because it shows the dependency of the amplification level on such parameters as wave velocity in surface soil layers, velocity contrast with deep layers, seismic wave type, incidence and damping.In this specific area of Nice, experimental measurements obtained for weak motion lead to strong site effects. A one-dimensional (1D) analytical analysis of amplification does not give a satisfactory estimation of the maximum reached levels. A boundary element model is then proposed considering different wave types (SH, P, SV) as the seismic loading. The alluvial basin is successively assumed as an isotropic linear elastic medium and an isotropic linear viscoelastic solid with Zener type behaviour (standard solid). The influence of frequency and incidence is analysed. The thickness of the surface layer, its mechanical properties, its general shape as well as the seismic wave type involved have a great influence on the maximum amplification and the frequency for which it occurs. For real earthquakes, the numerical results are in very good agreement with experimental measurements for each motion component. The boundary element method leads to amplification values very close to the actual ones and much larger than those obtained in the 1D case. Two-dimensional basin effects are then very strong and are well reproduced numerically.